Thursday, November 26, 2009

The length of an elven lifespan

One thing that gets me in fantasy literature: Elves, and how long elves live. Usually, we see elves living incredibly long lifespans "off-screen." Since they don't age, we see elves living thousands and thousands of years. Naturally, in the course of events that happen on-stage, they die off in fairly large numbers due to unnatural causes.

Elves aren't invincible. Some kinds of elves, such as Tolkien's elves, are immune to disease. These elves only die due to violence, lethal accidents, or suicide. Our first order estimate is therefore based on the most recent statistics for that - the WHO 2002 report on mortality. We see that 83 out of every 100,000 people die traumatically violent untimely deaths, and an additional 8 out of 100,000 starve to death.

With humans, this varies with age, but since elves are unaging and unchanging beings, we'll assume the average rate holds for all elves of any age. Thus, each year, 0.091% of all elves die. This means that the elven time of death is drawn from a simple exponential distribution with parameter λ = 0.00091.

The mean of an exponential distribution is simply 1/λ, so the average elven lifespan is 1100 years. The median elven lifespan is shorter - 760 years - and about 40% of elves live past their first millenium.

But 2002 was not that violent of a year. War, genocide, and famines tend to happen in short sharp "spikes." Only 2.8 people per 100,000 died as a result of war in 2002; over the course of the 20th century, about 10 billion people drew breath. 6 billion of those lived to see the end of it, and somewhere in the neighborhood of 200 million died in excessive spikes of "mass death" - famines and wars. That's 2,000 per 100,000 per 100 years; taking the appropriate 1/100th root, we get an average of 40 per 100,000.

If we take out today's war deaths and famine deaths and substitute an averaged value of 40 for "mass death" events, we get about 120 per 100,000. At λ = 0.0012, the average elven lifespan is 830 years, and the typical elf lives a mere 580 years. Only 30% of elves live to see out the end of their first millenium. One out of every 160,000 would live to see their tenth millenium.

Not all fantasy mythos leave elves immune to disease - and infectious disease represented 175 per 100,000 deaths in 2002. Historically, diseases have killed far more than violence and starvation, even among the healthy "young adult" population (smallpox, tuberculosis, measles, scarlet fever, malaria, outbreaks of various plagues - these can kill at any age) - so if elves aren't immune to disease, we would probably want to see λ to become substantially larger and the elven lifespan much shorter.

In the limiting case, where we consider lethal accidents, violence, and disease terms more typical to the dark ages? Well, let's just say that two or three centuries doesn't seem like such a short time for an elf to live, after all.